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Equivalence of information production and generalised entropies in complex processes

Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied. Here we show, that this perceived incompatibility is actually a...

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Autores principales: Hanel, Rudolf, Thurner, Stefan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10482297/
https://www.ncbi.nlm.nih.gov/pubmed/37672525
http://dx.doi.org/10.1371/journal.pone.0290695
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author Hanel, Rudolf
Thurner, Stefan
author_facet Hanel, Rudolf
Thurner, Stefan
author_sort Hanel, Rudolf
collection PubMed
description Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied. Here we show, that this perceived incompatibility is actually a misconception. For a broad class of processes, Boltzmann entropy –the log multiplicity– remains the valid entropy concept. However, for non-i.i.d. processes, Boltzmann entropy is not of Shannon form, −k∑(i)p(i) log p(i), but takes the shape of generalised entropies. We derive this result for all processes that can be asymptotically mapped to adjoint representations reversibly where processes are i.i.d. In these representations the information production is given by the Shannon entropy. Over the original sampling space this yields functionals identical to generalised entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes.
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spelling pubmed-104822972023-09-07 Equivalence of information production and generalised entropies in complex processes Hanel, Rudolf Thurner, Stefan PLoS One Research Article Complex systems with strong correlations and fat-tailed distribution functions have been argued to be incompatible with the Boltzmann-Gibbs entropy framework and alternatives, so-called generalised entropies, were proposed and studied. Here we show, that this perceived incompatibility is actually a misconception. For a broad class of processes, Boltzmann entropy –the log multiplicity– remains the valid entropy concept. However, for non-i.i.d. processes, Boltzmann entropy is not of Shannon form, −k∑(i)p(i) log p(i), but takes the shape of generalised entropies. We derive this result for all processes that can be asymptotically mapped to adjoint representations reversibly where processes are i.i.d. In these representations the information production is given by the Shannon entropy. Over the original sampling space this yields functionals identical to generalised entropies. The problem of constructing adequate context-sensitive entropy functionals therefore can be translated into the much simpler problem of finding adjoint representations. The method provides a comprehensive framework for a statistical physics of strongly correlated systems and complex processes. Public Library of Science 2023-09-06 /pmc/articles/PMC10482297/ /pubmed/37672525 http://dx.doi.org/10.1371/journal.pone.0290695 Text en © 2023 Hanel, Thurner https://creativecommons.org/licenses/by/4.0/This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
spellingShingle Research Article
Hanel, Rudolf
Thurner, Stefan
Equivalence of information production and generalised entropies in complex processes
title Equivalence of information production and generalised entropies in complex processes
title_full Equivalence of information production and generalised entropies in complex processes
title_fullStr Equivalence of information production and generalised entropies in complex processes
title_full_unstemmed Equivalence of information production and generalised entropies in complex processes
title_short Equivalence of information production and generalised entropies in complex processes
title_sort equivalence of information production and generalised entropies in complex processes
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10482297/
https://www.ncbi.nlm.nih.gov/pubmed/37672525
http://dx.doi.org/10.1371/journal.pone.0290695
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